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From "Radoslav Tsvetkov (JIRA)" <j...@apache.org>
Subject [jira] [Comment Edited] (MATH-878) G-Test (Log-Likelihood ratio - LLR test) in math.stat.inference
Date Mon, 15 Oct 2012 08:16:03 GMT

    [ https://issues.apache.org/jira/browse/MATH-878?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13476015#comment-13476015
] 

Radoslav Tsvetkov edited comment on MATH-878 at 10/15/12 8:14 AM:
------------------------------------------------------------------

Hi Ted, 
Signed Root LLR is a really good idea! I added the test (also in TestUtilsTest)

And some comment on signed rLLR:

In some cases of unexpectedly small similar p1 and p2 values 
or large anomalies of k11, ... counts it is desired to 
get additional information on the rate trough signed root LLR.
 
Signed root LLR has two advantages over the basic LLR: 

a) it is positive where k11 is bigger than expected, negative where it is 
lower.  This resolves your current problem. 

b) if there is no difference it is asymptotically normally distributed. 
This allows people to talk about "number of standard deviations" which is a 
more common frame of reference than the chi^2 distribution.
      
See Discussions at: ....
                
      was (Author: rtsvet):
    Hi Ted, 
Signed Root LLR is a really good idea! I added the test (also in TestUtilsTest)

And some comment on signed rLLR:
In some cases of unexpectedly small similar p1 and p2 values 
     * or large anomalies of k11, ... counts it is desired to 
     * get additional information on the rate trough signed root LLR.
     * 
     * Signed root LLR has two advantages over the basic LLR: 
     * a) it is positive where k11 is bigger than expected, negative where it is 
     * lower.  This resolves your current problem. 
     * b) if there is no difference it is asymptotically normally distributed. 
     * This allows people to talk about "number of standard deviations" which is a 
     * more common frame of reference than the chi^2 distribution.
     * 
     * See Discussions at: ....
                  
> G-Test (Log-Likelihood ratio - LLR test) in math.stat.inference
> ---------------------------------------------------------------
>
>                 Key: MATH-878
>                 URL: https://issues.apache.org/jira/browse/MATH-878
>             Project: Commons Math
>          Issue Type: New Feature
>    Affects Versions: 3.1, 3.2, 4.0
>         Environment: Netbeans
>            Reporter: Radoslav Tsvetkov
>              Labels: features, test
>             Fix For: 3.1
>
>         Attachments: MATH-878_gTest_12102012.patch, MATH-878_gTest_15102012.patch, vcs-diff16294.patch
>
>   Original Estimate: 24h
>  Remaining Estimate: 24h
>
> 1. Implementation of G-Test (Log-Likelihood ratio LLR test for independence and goodnes-of-fit)
> 2. Reference: http://en.wikipedia.org/wiki/G-test
> 3. Reasons-Usefulness: G-tests are tests are increasingly being used in situations where
chi-squared tests were previously recommended. 
> The approximation to the theoretical chi-squared distribution for the G-test is better
than for the Pearson chi-squared tests. In cases where Observed >2*Expected for some cell
case, the G-test is always better than the chi-squared test.
> For testing goodness-of-fit the G-test is infinitely more efficient than the chi squared
test in the sense of Bahadur, but the two tests are equally efficient in the sense of Pitman
or in the sense of Hodge and Lehman. 

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